Method of exhaust temperature prediction

ABSTRACT

A torque requesting module generates a torque request for an engine based on driver input. A model predictive control (MPC) module: identifies sets of possible target values based on the torque request, each of the sets of possible target values including target effective throttle area percentage; determines predicted operating parameters for the sets of possible target values, respectively; determines cost values for the sets of possible target values, respectively; selects one of the sets of possible target values based on the cost values; and sets target values based on the possible target values of the selected one of the sets, respectively, the target values including a target pressure ratio across the throttle valve. A target area module determines a target opening area of the throttle valve based on the target effective throttle area percentage ratio. A throttle actuator module controls the throttle valve based on the target opening.

FIELD

The present disclosure relates to internal combustion engines and moreparticularly to engine control system development for vehicles.

BACKGROUND

The background description provided here is for the purpose of generallypresenting the context of the disclosure. Work of the presently namedinventors, to the extent it is described in this background section, aswell as aspects of the description that may not otherwise qualify asprior art at the time of filing, are neither expressly nor impliedlyadmitted as prior art against the present disclosure.

Internal combustion engines combust an air and fuel mixture withincylinders to drive pistons, which produces drive torque. Air flow intothe engine is regulated via a throttle. More specifically, the throttleadjusts throttle area, which increases or decreases air flow into theengine. As the throttle area increases, the air flow into the engineincreases. A fuel control system adjusts the rate that fuel is injectedto provide a desired air/fuel mixture to the cylinders and/or to achievea desired torque output. Increasing the amount of air and fuel providedto the cylinders increases the torque output of the engine.

When developing an engine for vehicle production, the engine must becalibrated to ensure proper operation. Part of what is considered properoperation is maintaining safe conditions for engine hardwareparticularly the hardware related to emissions. Each particular enginecalibration is a result of testing several operation parameters byvarying the parameters and collecting the results as data. Thecombinations of operation parameters that allow the engine to runoutside of the specified temperatures, for example, are deemed unsafefor the engine hardware. Therefore, the resultant calibration will notallow the engine to operate at those particular parameters. The testingis expanded for each combination of parameters until enough data iscollected for an engine map. The constant reiteration of testing eachvariable operation parameter results in a great deal of test timerequiring expensive test facilities and man hours.

While the current method of calibrating engines is primarily successful,calibrators are required to invest hundreds of man hours and dynamometertest cell hours for data acquisition required for engine mapping.Therefore, a new method of engine calibration is necessary that is moreefficient and requires less test time and hours to develop an enginecalibration.

SUMMARY

A method for estimating an exhaust temperature of an intern combustionengine comprises acquiring a current exhaust temperature for a knownfuel equivalent ratio (EQR) and a known spark timing (CA50 offset),setting a normalized temperature ratio surface to the current exhausttemperature, the known EQR, and the known CA50 offset, and providing apredicted exhaust temperature produced by an alternative EQR and analternative CA50 offset based on the normalized temperature ratiosurface.

In another example of the present invention, the method includesproviding an equivalent EQR that along with the known CA50 offsetproduces a known exhaust temperature limit based on the normalizedtemperature ratio surface.

In yet another example of the present invention, the method includesproviding an equivalent CA50 offset that along with the known EQRproduces a known exhaust temperature limit based on the normalizedtemperature ratio surface.

In yet another example of the present invention, acquiring a currentexhaust temperature for a known EQR and a known CA50 offset furthercomprises acquiring a current exhaust temperature for a known fuel EQRand known CA50 wherein the known EQR is a ratio of an actual air/fuelratio to a stoichiometric air/fuel ratio.

In yet another example of the present invention, acquiring a currentexhaust temperature for a known EQR and a known CA50 offset furthercomprises acquiring a current exhaust temperature for a known fuel EQRand known CA50 wherein the known CA50 offset is a number of crankshaftdegrees from a crankshaft position at which 50% of an air/fuel mass iscombusted.

In yet another example of the present invention, setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset further comprises setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the known EQR is the inverseof Lambda, the normalized temperature ratio surface (Z(I,J)) is definedby the following equations:

Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+D

Z(I,J)=Y(J)*(E*CA50² +F*CA50+G), and

A, B, C, D, E, F, and G are constants specific to the engine.

In yet another example of the present invention, setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset further comprises setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the known EQR is the inverseof Lambda and the normalized temperature ratio surface (Z(I,J)) isdefined by the following equations:

Y(J)=−5.1666*Lambda³+12.307*Lambda²−9.0429*Lambda+2.901

Z(I,J)=Y(J)*(1e ⁻⁴ *CA50²+0.0048*CA50+1.0005).

In yet another example of the present invention, setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset further comprises setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the normalized temperatureratio is a ratio of a current exhaust temperature to an exhausttemperature when EQR=1 and CA50=8.5°.

Further objects, aspects and advantages of the present invention willbecome apparent by reference to the following description and appendeddrawings wherein like reference numbers refer to the same component,element or feature.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an example engine systemaccording to the present disclosure;

FIG. 2 is a three axis graph depicting a normalized temperature surfaceas a function of fuel ratio and spark ignition timing; and

FIG. 3 is a functional block diagram of a method of calibrating anengine system according to the present disclosure.

DETAILED DESCRIPTION

Referring now to FIG. 1, a functional block diagram of an example enginesystem 100 is presented. The engine system 100 includes an engine 102that combusts an air/fuel mixture to produce drive torque for a vehiclebased on driver input from a driver input module 104. The engine 102 maybe a gasoline spark ignition internal combustion engine.

Air is drawn into an intake manifold 110 through a throttle valve 112.For example only, the throttle valve 112 may include a butterfly valvehaving a rotatable blade. An engine control module (ECM) includessoftware programs for controlling engine operations based on driver andsensor input. The ECM 114 controls a throttle actuator module 116, whichregulates opening of the throttle valve 112 to control the amount of airdrawn into the intake manifold 110. The software programs of the ECM 114include logic code written by engine calibrators. The logic code is thedecision making algorithms that receive input from the several sensorson the engine, transmission, and vehicle and communicate operationsignals to the various actuators that control the powertrain operation.

Air from the intake manifold 110 is drawn into cylinders of the engine102. While the engine 102 may include multiple cylinders, forillustration purposes a single representative cylinder 118 is shown. Forexample only, the engine 102 may include 2, 3, 4, 5, 6, 8, 10, and/or 12cylinders. The ECM 114 may instruct a cylinder actuator module 120 toselectively deactivate some of the cylinders, which may improve fueleconomy under certain engine operating conditions.

The engine 102 may operate using a four-stroke cycle. The four strokes,described below, may be referred to as the intake stroke, thecompression stroke, the combustion stroke, and the exhaust stroke.During each revolution of a crankshaft (not shown), two of the fourstrokes occur within the cylinder 118. Therefore, two crankshaftrevolutions are necessary for the cylinder 118 to experience all four ofthe strokes.

During the intake stroke, air from the intake manifold 110 is drawn intothe cylinder 118 through an intake valve 122. The ECM 114 controls afuel actuator module 124, which regulates fuel injection to achieve atarget air/fuel ratio. Fuel may be injected into the intake manifold 110at a central location or at multiple locations, such as near the intakevalve 122 of each of the cylinders. In various implementations (notshown), fuel may be injected directly into the cylinders or into mixingchambers associated with the cylinders. The fuel actuator module 124 mayhalt injection of fuel to cylinders that are deactivated.

The injected fuel mixes with air and creates an air/fuel mixture in thecylinder 118. During the compression stroke, a piston (not shown) withinthe cylinder 118 compresses the air/fuel mixture. A spark actuatormodule 126 energizes a spark plug 128 in the cylinder 118 based on asignal from the ECM 114, which ignites the air/fuel mixture. The timingof the spark may be specified relative to the time when the piston is atits topmost position, referred to as top dead center (TDC).

The spark actuator module 126 may be controlled by a timing signalspecifying how far before or after TDC to generate the spark. Becausepiston position is directly related to crankshaft rotation, operation ofthe spark actuator module 126 may be synchronized with crankshaft angle.Generating spark may be referred to as a firing event. The sparkactuator module 126 may have the ability to vary the timing of the sparkfor each firing event. The spark actuator module 126 may vary the sparktiming for a next firing event when the spark timing is changed betweena last firing event and the next firing event. The spark actuator module126 may halt provision of spark to deactivated cylinders.

During the combustion stroke, the combustion of the air/fuel mixturedrives the piston away from TDC, thereby driving the crankshaft. Thecombustion stroke may be defined as the time between the piston reachingTDC and the time at which the piston reaches bottom dead center (BDC).During the exhaust stroke, the piston begins moving away from BDC andexpels the byproducts of combustion through an exhaust valve 130. Thebyproducts of combustion are exhausted from the vehicle via an exhaustsystem 134.

The intake valve 122 may be controlled by an intake camshaft 140, whilethe exhaust valve 130 may be controlled by an exhaust camshaft 142. Invarious implementations, multiple intake camshafts (including the intakecamshaft 140) may control multiple intake valves (including the intakevalve 122) for the cylinder 118 and/or may control the intake valves(including the intake valve 122) of multiple banks of cylinders(including the cylinder 118). Similarly, multiple exhaust camshafts(including the exhaust camshaft 142) may control multiple exhaust valvesfor the cylinder 118 and/or may control exhaust valves (including theexhaust valve 130) for multiple banks of cylinders (including thecylinder 118). In various other implementations, the intake valve 122and/or the exhaust valve 130 may be controlled by devices other thancamshafts, such as camless valve actuators. The cylinder actuator module120 may deactivate the cylinder 118 by disabling opening of the intakevalve 122 and/or the exhaust valve 130.

The time when the intake valve 122 is opened may be varied with respectto piston TDC by an intake cam phaser 148. The time when the exhaustvalve 130 is opened may be varied with respect to piston TDC by anexhaust cam phaser 150. A phaser actuator module 158 may control theintake cam phaser 148 and the exhaust cam phaser 150 based on signalsfrom the ECM 114. When implemented, variable valve lift (not shown) mayalso be controlled by the phaser actuator module 158.

The engine system 100 may include a turbocharger that includes a hotturbine 160-1 that is powered by hot exhaust gases flowing through theexhaust system 134. The turbocharger also includes a cold air compressor160-2 that is driven by the turbine 160-1. The compressor 160-2compresses air leading into the throttle valve 112. In variousimplementations, a supercharger (not shown), driven by the crankshaft,may compress air from the throttle valve 112 and deliver the compressedair to the intake manifold 110.

A wastegate 162 may allow exhaust to bypass the turbine 160-1, therebyreducing the boost (the amount of intake air compression) provided bythe turbocharger. A boost actuator module 164 may control the boost ofthe turbocharger by controlling opening of the wastegate 162. In variousimplementations, two or more turbochargers may be implemented and may becontrolled by the boost actuator module 164.

An air cooler (not shown) may transfer heat from the compressed aircharge to a cooling medium, such as engine coolant or air. An air coolerthat cools the compressed air charge using engine coolant may bereferred to as an intercooler. An air cooler that cools the compressedair charge using air may be referred to as a charge air cooler. Thecompressed air charge may receive heat, for example, via compressionand/or from components of the exhaust system 134. Although shownseparated for purposes of illustration, the turbine 160-1 and thecompressor 160-2 may be attached to each other, placing intake air inclose proximity to hot exhaust.

The engine system 100 may include an exhaust gas recirculation (EGR)valve 170, which selectively redirects exhaust gas back to the intakemanifold 110. The EGR valve 170 may be located upstream of theturbocharger's turbine 160-1. The EGR valve 170 may be controlled by anEGR actuator module 172 based on signals from the ECM 114.

A position of the crankshaft may be measured using a crankshaft positionsensor 180. A rotational speed of the crankshaft (an engine speed) maybe determined based on the crankshaft position. A temperature of theengine coolant may be measured using an engine coolant temperature (ECT)sensor 182. The ECT sensor 182 may be located within the engine 102 orat other locations where the coolant is circulated, such as a radiator(not shown).

A pressure within the intake manifold 110 may be measured using amanifold absolute pressure (MAP) sensor 184. In various implementations,engine vacuum, which is the difference between ambient air pressure andthe pressure within the intake manifold 110, may be measured. A massflow rate of air flowing into the intake manifold 110 may be measuredusing a mass air flow (MAF) sensor 186. In various implementations, theMAF sensor 186 may be located in a housing that also includes thethrottle valve 112.

The throttle actuator module 116 may monitor the position of thethrottle valve 112 using one or more throttle position sensors (TPS)190. A pressure of air input to the throttle valve 112 may be measuredusing a throttle inlet air pressure (TIAP) sensor 191. An ambienttemperature of air being drawn into the engine 102 may be measured usingan intake air temperature (IAT) sensor 192. The engine system 100 mayalso include one or more other sensors 193, such as an ambient humiditysensor, one or more knock sensors, a compressor outlet pressure sensorand/or a throttle inlet pressure sensor, a wastegate position sensor, anEGR position sensor, and/or one or more other suitable sensors. The ECM114 may use signals from the sensors to make control decisions for theengine system 100.

The ECM 114 may communicate with a transmission control module 194 tocoordinate shifting gears in a transmission (not shown). For example,the ECM 114 may reduce engine torque during a gear shift. The ECM 114may communicate with a hybrid control module 196 to coordinate operationof the engine 102 and an electric motor 198.

The electric motor 198 may also function as a generator, and may be usedto produce electrical energy for use by vehicle electrical systemsand/or for storage in a battery. In various implementations, variousfunctions of the ECM 114, the transmission control module 194, and thehybrid control module 196 may be integrated into one or more modules.

Each system that varies an engine parameter may be referred to as anengine actuator. For example, the throttle actuator module 116 mayadjust opening of the throttle valve 112 to achieve a target throttleopening area. The spark actuator module 126 controls the spark plugignition to achieve a target spark timing relative to piston TDC. Thefuel actuator module 124 controls the fuel injectors to achieve targetfueling parameters. The phaser actuator module 158 may control theintake and exhaust cam phasers 148 and 150 to achieve target intake andexhaust cam maximum opening positions, respectively. The boost actuatormodule 164 controls the wastegate 162 to achieve a target wastegateopening area. The cylinder actuator module 120 controls cylinderdeactivation to achieve a target number of activated or deactivatedcylinders.

One of the many tasks assigned to a calibration of the vehiclepowertrain is to protect the powertrain hardware from damage. Oneexample of protecting an engine through calibration is utilizing anengine speed limiter to keep the engine from spinning too fast. Theengine speed limiter works by cutting fuel and/or spark ignition to theengine when a particular RPM is reached.

Another example of protecting engine hardware is limiting thetemperature at which the engine hardware operates. Turning now to FIG.2, a graph 200 of the relationship between two engine operatingparameters and the temperature of the collection area of the exhaustmanifold. The particular engine operating parameters or actuators ofprominence here are the spark actuator module 126 and the fuel actuatormodule 124. The control logic that the powertrain calibrators programincludes manipulation of a fuel parameter, the fuel equivalence ratio(EQR), and a spark ignition timing parameter CA50 (the angle of thecrankshaft at which half of the combustible air/fuel mass is burned inthe cylinder) 204. EQR is used to control the amount of fuel that isinjected into the intake manifold or cylinder by the fuel injectors. TheEQR is the ratio of the actual amount of fuel injected to the amount offuel required for stoichiometric combustion. An EQR that is greater than1 indicates a fuel rich air/fuel mixture. If the EQR is less than 1, theair/fuel mixture is lean. In terms of the effect on exhaust temperatureratio 206, each of the lean and rich EQR has a reducing effect onexhaust temperature ratio 206 albeit for different reasons. A rich EQRburns all the fuel injected in the cylinder to the point that the oxygenruns out. The remaining unburnt fuel is exhausted with the burnt gasesto the exhaust manifold. The unburnt fuel then has a cooling effect onthe exhaust manifold and catalyst. A lean EQR, while burning all thefuel injected into the cylinder, simply does not burn as much fuel aswhen the EQR is 1 and therefore has reduced temperatures and pressuresof the gases exhausting from the cylinder into the exhaust manifold andcatalyst.

Additionally, a spark timing parameter is adjusted by calibrators toachieve particular performance outcomes. The spark timing parameter CA50offset 204 is the number of degrees of advanced or retarded spark fromCA50. For example, retarding spark ignition 10° delays combustioncompared to the rotational position of the crankshaft and therefore theposition of the piston in the cylinder 118 and of the exhaust valve 130.The delay in spark ignition delays the combustion event such that lessof the fuel/air mass is burning in the cylinder and more of the fuel/airmass is burning as the mixture leaves the cylinder through the exhaustport and into the exhaust manifold. As a result, retarding spark 212 forthe most part increases the temperature of the exhaust manifold andcatalyst due to the progressively increasing pressure and temperature ofthe mass combusting while it goes through the exhaust manifold 134.Alternatively, advancing spark 214 results in more of the combustionoccurring within the cylinder and therefore lower exhaust temperatures.

The graph 200 includes a normalized temperature surface 216 forcalibrating safe exhaust temperature ratio 206 for a particular variableLambda 202 and CA50 offset 204 parameters. The vertical axis 206 is atemperature ratio which is defined as a ratio of a current exhausttemperature to an exhaust temperature when EQR=1 and CA50=8.5°.Therefore, when the current exhaust temperature is greater than theexhaust temperature when EQR=1 and CA50=8.5° then the temperature ratiois greater than 1. Likewise, when the current exhaust temperature isless than the exhaust temperature when EQR=1 and CA50=8.5° then thetemperature ratio is less than 1.

The value on a first horizontal axis is for Lambda 202. Lambda 202 isthe inverse of EQR. Therefore, a lean air/fuel ratio 208 will have alambda 202 value greater than 1. A rich air/fuel ratio 210 will have alambda 202 value less than 1.

The value displayed in the graph 200 on the second horizontal axis isCA50 204 which is the degrees of spark timing offset from 8.5°. Valuesgreater than zero represent spark retard while values less than zerorepresent spark advance.

The normalized temperature surface 216 is derived from a formulatedequation as shown:

Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+D

Z(I,J)=Y(J)*(E*CA50² +F*CA50+G)

Where A, B, C, D, E, F, and G are constants that are derived from enginetesting and are specific to a particular engine configuration. Forexample, the constants used to derive the normalized temperature surface216 shown in FIG. 2 are as follows:

-   -   A=−5.1666    -   B=12.3070    -   C=−9.0429    -   D=2.9010    -   E=1e⁻⁴    -   F=0.0048    -   G=1.0005        Whereas these constants are applicable to many different        engines, a minimal amount of testing is required to more        precisely calibrate the constants for some engine applications.

Turning now to FIG. 3 with continuing reference to FIG. 2, a method forcalibrating an engine for exhaust temperature protection is depicted andwill now be described. The method 300 begins with a first step 310 ofcollecting a data point of a current exhaust temperature for a known EQR202 and a known CA50 offset 204. A second step 312 includes applying thedata point of the first step 310 to the normalized temperature surface216. From the second step 312, the method 300 continues to a third step314 of predicting the exhaust temperature under a new set of EQR 202 andCA50 offset 204 parameters. Additionally, the method 300 can continue toa fourth step 314 predicting an EQR 202 given a known CA50 offset 204and a known exhaust temperature limit or predicting CA50 offset 204given a known EQR 202 and a known exhaust temperature limit.

The foregoing description of the invention is merely exemplary in natureand variations that do not depart from the gist of the invention are andare intended to be within the scope of the invention. Such variationsare not to be regarded as a departure from the spirit and scope of theinvention and the following claims.

We claim:
 1. A method for estimating an exhaust temperature of an interncombustion engine, the method comprising: acquiring a current exhausttemperature for a known fuel equivalent ratio (EQR) and a known sparktiming (CA50 offset); setting a normalized temperature ratio surface tothe current exhaust temperature, the known EQR, and the known CA50offset, and providing a predicted exhaust temperature produced by analternative EQR and an alternative CA50 offset based on the normalizedtemperature ratio surface.
 2. The method of claim 1 further comprisesproviding an equivalent EQR that along with the known CA50 offsetproduces a known exhaust temperature limit based on the normalizedtemperature ratio surface.
 3. The method of claim 1 further comprisesproviding an equivalent CA50 offset that along with the known EQRproduces a known exhaust temperature limit based on the normalizedtemperature ratio surface.
 4. The method of claim 1 wherein acquiring acurrent exhaust temperature for a known EQR and a known CA50 offsetfurther comprises acquiring a current exhaust temperature for a knownfuel EQR and known CA50 wherein the known EQR is a ratio of an actualair/fuel ratio to a stoichiometric air/fuel ratio.
 5. The method ofclaim 1 wherein acquiring a current exhaust temperature for a known EQRand a known CA50 offset further comprises acquiring a current exhausttemperature for a known fuel EQR and known CA50 wherein the known CA50offset is a number of crankshaft degrees from a crankshaft position atwhich 50% of an air/fuel mass is combusted.
 6. The method of claim 1wherein setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset furthercomprises setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset, andwherein the known EQR is the inverse of Lambda, the normalizedtemperature ratio surface (Z(I,J)) is defined by an equation as follows:Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+DZ(I,J)=Y(J)*(E*CA50² +F*CA50+G), and A, B, C, D, E, F, and G areconstants specific to the engine.
 7. The method of claim 1 whereinsetting a normalized temperature ratio surface to the current exhausttemperature, the known EQR, and the known CA50 offset further comprisessetting a normalized temperature ratio surface to the current exhausttemperature, the known EQR, and the known CA50 offset, and wherein theknown EQR is the inverse of Lambda and the normalized temperature ratiosurface (Z(I,J)) is defined by an equation as follows:Y(J)=−5.1666*Lambda³+12.307*Lambda²−9.0429*Lambda+2.901Z(I,J)=Y(J)*(1e ⁻⁴ *CA50²+0.0048*CA50+1.0005).
 8. The method of claim 1wherein setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset furthercomprises setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset, andwherein the normalized temperature ratio is a ratio of a current exhausttemperature to an exhaust temperature when EQR=1 and CA50=8.5°.
 9. Amethod for estimating an exhaust temperature of an internal combustionengine, the method comprising: acquiring a current exhaust temperaturefor a known fuel equivalent ratio (EQR) and a known spark timing (CA50offset); setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset; providinga predicted exhaust temperature produced by an alternative EQR and analternative CA50 offset based on the normalized temperature ratiosurface; providing an equivalent EQR that along with the known CA50offset produces a known exhaust temperature limit based on thenormalized temperature ratio surface, and providing an equivalent CA50offset that along with the known EQR produces a known exhausttemperature limit based on the normalized temperature ratio surface. 10.The method of claim 9 wherein acquiring a current exhaust temperaturefor a known EQR and a known CA50 offset further comprises acquiring acurrent exhaust temperature for a known fuel EQR and known CA50 whereinthe known EQR is a ratio of an actual air/fuel ratio to a stoichiometricair/fuel ratio.
 11. The method of claim 9 wherein acquiring a currentexhaust temperature for a known EQR and a known CA50 offset furthercomprises acquiring a current exhaust temperature for a known fuel EQRand known CA50 wherein the known CA50 offset is a number of crankshaftdegrees from a crankshaft position at which 50% of an air/fuel mass iscombusted.
 12. The method of claim 9 wherein setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset further comprises setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the known EQR is the inverseof Lambda, the normalized temperature ratio surface (Z(I,J)) is definedby an equation as follows:Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+DZ(I,J)=Y(J)*(E*CA50² +F*CA50+G), and A, B, C, D, E, F, and G areconstants specific to the engine.
 13. The method of claim 9 whereinsetting a normalized temperature ratio surface to the current exhausttemperature, the known EQR, and the known CA50 offset further comprisessetting a normalized temperature ratio surface to the current exhausttemperature, the known EQR, and the known CA50 offset, and wherein theknown EQR is the inverse of Lambda and the normalized temperature ratiosurface (Z(I,J)) is defined by an equation as follows:Y(J)=−5.1666*Lambda³+12.307*Lambda²−9.0429*Lambda+2.901Z(I,J)=Y(J)*(1e ⁻⁴ *CA50²+0.0048*CA50+1.0005).
 14. The method of claim 9wherein setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset furthercomprises setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset, andwherein the normalized temperature ratio is a ratio of a current exhausttemperature to an exhaust temperature when EQR=1 and CA50=8.5°.
 15. Amethod for estimating an exhaust temperature of an intern combustionengine, the method comprising: acquiring a current exhaust temperaturefor a known fuel equivalent ratio (EQR) and a known spark timing (CA50offset); setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset, andwherein the known EQR is the inverse of Lambda, the normalizedtemperature ratio surface (Z(I,J)) is defined by an equation as follows:Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+DZ(I,J)=Y(J)*(E*CA50² +F*CA50+G), and A, B, C, D, E, F, and G areconstants; providing a predicted exhaust temperature produced by analternative EQR and an alternative CA50 offset based on the normalizedtemperature ratio surface, and providing an equivalent EQR that alongwith the known CA50 offset produces a known exhaust temperature limitbased on the normalized temperature ratio surface.
 16. The method ofclaim 15 further comprises providing an equivalent CA50 offset thatalong with the known EQR produces a known exhaust temperature limitbased on the normalized temperature ratio surface.
 17. The method ofclaim 15 wherein acquiring a current exhaust temperature for a known EQRand a known CA50 offset further comprises acquiring a current exhausttemperature for a known fuel EQR and known CA50 wherein the known EQR isa ratio of an actual air/fuel ratio to a stoichiometric air/fuel ratio.18. The method of claim 15 wherein acquiring a current exhausttemperature for a known EQR and a known CA50 offset further comprisesacquiring a current exhaust temperature for a known fuel EQR and knownCA50 wherein the known CA50 offset is a number of crankshaft degreesfrom a crankshaft position at which 50% of an air/fuel mass iscombusted.
 19. The method of claim 18 wherein setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the known EQR is the inverseof Lambda, the normalized temperature ratio surface (Z(I,J)) is definedby an equation as follows:Y(J)=A*Lambda³ +B*Lambda² +C*Lambda+DZ(I,J)=Y(J)*(E*CA50² +F*CA50+G), and A, B, C, D, E, F, and G areconstants specific to an engine further comprises setting a normalizedtemperature ratio surface to the current exhaust temperature, the knownEQR, and the known CA50 offset, and wherein the known EQR is the inverseof Lambda and the normalized temperature ratio surface (Z(I,J)) isdefined by an equation as follows:Y(J)=−5.1666*Lambda³+12.307*Lambda²−9.0429*Lambda+2.901Z(I,J)=Y(J)*(1e ⁻⁴ *CA50²+0.0048*CA50+1.0005).
 20. The method of claim15 wherein setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset furthercomprises setting a normalized temperature ratio surface to the currentexhaust temperature, the known EQR, and the known CA50 offset, andwherein the normalized temperature ratio is a ratio of a current exhausttemperature to an exhaust temperature when EQR=1 and CA50=8.5°.